Amanda Agan and Alexander T. Tabarrok (Both of George Mason University Economics Department) have posted What are Private Governments Worth? on SSRN. Here's the abstract:

Homeowners associations (HOAs) and other local private governments are expanding in number both in the United States and around the world. Local private governments are also expanding in scope, with many offering private security and a few even offering services such as day care, schools, and local courts to arbitrate homeowner disputes. How valuable are those services to association-members? Our data indicate that houses in HOAs in Northern Virginia are worth, on average, more than 5 percent more than similar houses in the same neighborhood but outside of HOAs. Given those large advantages, it is not surprising that HOAs are growing rapidly.